Private Quantum Subsystems and Quasiorthogonal Operator Algebras

TL;DR

This paper extends the concept of private quantum subsystems to Abelian subgroups of the n-qubit Pauli group, linking quantum privacy with quasiorthogonal operator algebras using group and operator theory tools.

Contribution

It introduces private subsystems for Abelian Pauli groups and connects quantum privacy with quasiorthogonal operator algebra theory.

Findings

Private subsystems exist without private subspaces.

Connection established between quantum privacy and quasiorthogonal operator algebras.

Generalization of previous private quantum subsystem examples.

Abstract

We generalize a recently discovered example of a private quantum subsystem to find private subsystems for Abelian subgroups of the $n$-qubit Pauli group, which exist in the absence of private subspaces. In doing so, we also connect these quantum privacy investigations with the theory of quasiorthogonal operator algebras through the use of tools from group theory and operator theory.